GGI, 28-30 September 2006 Advances in in Precision Precision Tests Tests Advances and and Experimental Gravitation in Gravitation in Space Space Experimental Alternative Theories Theories of of Alternative Gravity and Cosmology Gravity and Cosmology Gabriele VENEZIANO Gabriele VENEZIANO (CERN & Collège de France) (CERN & Collège de France)
Outline Outline 1. Why alternatives? 2. From quantum strings to classical “gravity” 3. Light scalars? 4. Large extra dimensions? 5. Conclusions
Why alternatives? Why alternatives? Einstein’s General Relativity General Relativity (GR) is a very successful framework for describing gravity in most physical situations: our Standard Model Standard Model of gravitational interactions, tested by now to O(10 -3 ) accuracy It seems to be applicable, equally well, to isolated systems, to waves in empty space, and to the Universe as a whole. The universal attractive nature of gravity is responsible for the growth of small initial perturbations into the large-scale structure of our Universe. There is no apparent reason for mistrusting GR in yet unexplored regimes…but
Experimental puzzles abund abund Experimental puzzles 1. What is dark matter? 2. What is dark energy? 3. What’s the origin of the initial inhomogeneities? 4. What’s the origin of baryon asymmetry? 5. What’s the origin of HECR and GRB? 6. …
Theoretical puzzles too! Theoretical puzzles too! Gravitational attraction is also responsible for gravitational collapse, formation of black holes, and of singularities. Theorems by Hawking & Penrose imply that, under mild assumptions, smooth «initial conditions» lead, inevitably inevitably, to , to space-time singularities singularities, e.g. 1. The singularity behind a black-hole black-hole horizon 2. The cosmological The cosmological (big bang) (big bang) singularity 2. Q 1 : What happens to singularities when we take quantum effects into account? Answer not known: have you ever heard about QGD? Q 2 : Can we reconcile General Relativity & Quantum Mechanics?
At present, the leading candidate for reconciling GR and QM is (Super)String Theory As such, it should provide answers to those hard questions
From quantum strings to classical “ “gravity gravity” ” From quantum strings to classical Classical strings (e.g. cosmic strings) do gravitate but • that’s not what we are after. By contrast: Quantum (fundamental) strings induce gravity: how come? • It’s the consequence of some remarkable quantum miracles! •
Quantum miracles: I. Finite Finite Size Size Quantum miracles: I. Classical relativistic strings with tension T T may have any size L L and any mass M ~T L c M ~T L c -2 -2 ; Quantum strings have a minimal (optimal) size L L s s (Cf. Bohr radius), given by L L s = hc/T hc/T * ) . 2 = s2 This length appears naturally in the (dimensionless, quantum) action of a string: * ) Note analogy with L L P = hG/c 3 3 (if G-->c 4 /T) 2 = hG/c P2
QST QFT QST QFT L s L s L s This finite string size, L s , is responsible for the smearing of interactions over finite regions of spacetime and for the consequent disappearance of UV divergences
Quantum miracles: II. Finite Finite Spin Spin Quantum miracles: II. While classical string cannot have angular momentum without also having a finite size/mass, quantum strings may have up to 2 2 units units of J of J without without acquiring mass mass: Cf. Casimir effect
Quantum Spectrum Quantum Spectrum Classical boundary Classical boundary (at tree level) (at tree level) fermions J fermions J J J Classically Classically 2h 2h forbidden forbidden 3/2h 3/2h Classically Classically h h allowed allowed 1/2h 1/2h M 2 M 2 2h 2h M 2 M 2
In particular.. => m=0, J = 1 => photon and other gauge bosons ⇒ m=0, J = 2 => graviton, ⇒ m=0, J = 0 => dilaton Integer-J massless states => carriers of interactions carriers of interactions; 1/2-integer-J massless (light)states => constituents constituents of of matter matter
Combining both miracles provides A unified unified and finite finite theory of elementary particles, and of their gauge & gravitational interactions …an old challenge as we know from CSI… Episode 101 - “Blink” Detective Mac Taylor discovers the body of a missing woman in Brooklyn Heights. When he discovers a second victim on a garbage barge, his investigation leads him to a serial killer who “imprisons” his victims. Grappling with memories of his own wife, Taylor follows the killer’s trail to a live victim. A woman who cannot move, feel, or speak. A woman who stretches stretches Veneziano Veneziano’ ’s s theory of theory of quantum physics to its outer limit, challenging Taylor to prove that “everything is everything is quantum physics to its outer limit connected connected.” But there there are are other other quantum news.. quantum news.. But
Classical strings can move consistently in any ambient space-time; Quantum strings require particular background space-times in order to avoid lethal anomalies. E. g.: a Minkowskian space-time must have 1 time and 9 space dimensions. Six of them are presumably compact. No free parameters: replaced by scalar fields whose expectation values provide (dynamically?) the «Constants of Nature». For instance, the fine-structure constant α and G N T are fixed by the dilaton and by the various compactification radii. String theory goes one step further than GR by making everything, including microphysics, soft (T. Damour)
Light scalars? Light scalars? Some J=0 massless strings (at tree level) are there • irrespectively of compactification: the dilaton φ and its SUSY (pseudoscalar) partner, the (KR) axion σ < φ > controls the importance of loops (analogue of gauge • coupling in QFT) but φ itself is a bona-fide field associated with a spin 0 particle => Gauge and gravitational couplings can be, in principle, • functions of space and time. As such, the dilaton is responsible for an extra attractive • force between two bodies A and B whose strength (in units of G N ) is given by: This “5th force” violates the EP, universality of free fall
The compactification moduli compactification moduli The Sizes and shapes of the extra dimensions are controlled by • a bunch of (pseudo)scalar fields called moduli, usually also massless at tree level (or even to all orders in PT) They may acquire a mass from higher order (or non- • perturbative) effects (only “protected” by SUSY) If they end up being “heavy” they are not so interesting • If they end up being very light (or massless) we may • distinguish two cases: 1. They have been light and coupled O(G N ) in the early universe, acquired a mass later => interesting for early cosmology, not for today’s experiments 2. They may be light and very weakly coupled (< G N ) even today => interesting for dark energy, violations of Equivalence Principle, variations of “constants”
1. Light, gravitationally coupled scalar fields in EU 1. Light, gravitationally coupled scalar fields in EU Early cosmology would not be described by GR, but by the appropriate (multidimensional) effective lagrangian of string theory, even in its classical regimes. Basis of unconventional cosmologies such as the pre-big bang or expyrotic/cyclic scenarios Typically, a classical (but not GR) pre-bang phase gets connected to a standard (GR) post-bang cosmology through a “quantum bridge”, a high-curvature phase in which an effective field theory (let alone GR) description makes no sense These cosmologies do not (seem to) give the right spectrum of adiabatic density perturbations that slow-roll inflation provides: blue, rather than nearly scale-invariant. Example of tensor perturbations (GW)
Cosmic superstrings
Can the axion axion save the day? save the day? Can the The (KR) axion σ can have a scale-invariant spectrum. Its • tilt, (n σ -1), depends on evolution of the internal dimensions in pre-bang phase: SI spectrum corresponds to a “symmetric” evolution of all nine spatial-dimensions Unfortunately, axion perturbations do not talk, to first • order, to metric perturbations (entropic, isocurvature fluctuations) => bad predictions for acoustic peaks The way to rescue these cosmologies is to have the axion • play the role of the “curvaton” by first becoming a relevant fraction of the total energy density, and by then decaying (before Nucleosynthesis) Gives agreement with present CMB data and specific • expectations on T-perturbations, non-gaussianity.
TT and TE (E-mode of polarization) correlations from WMAP B-mode needed to test different theories
2. Some scalar fields are light even today 2. Some scalar fields are light even today (and coupled << G N ) (and coupled << G N ) Interesting for: Dark energy, Dark energy, Violations of EP, Violations of EP, Variations of “ “constants constants” ” Variations of
Dilaton as as dark energy dark energy? ? Dilaton We have to settle first the question of its coupling to matter and of possible EP-violations • By supersymmetry, φ is massless to all orders in perturbation theory • Its perturbative coupling to matter is larger than gravity and non-universal This problem goes under the name of the “Dilaton (moduli) Stabilization Problem” in String Theory
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